If I see a hundred elephants and fifty of them are grey I'd say the probability of an elephant being grey is 50%. And my certainty of that probability is high.
However, if I see two elephants and one of them is grey. Still the probability is 50%. But my certaintity of this is low.
Are there any AI models where not only the probability is given by the AI but it's certainty is also?
"Certainty" might be thought of as the probability that the probability is correct.
This could go up more levels.
Is there any advantage in doing this?
One way I can envisage this working is instead of a weight, the NN stores two integers $(P,N)$ which represent positive and negative evidence and the weight is given by $P/(P+N)$. And each iteration $P$ or $N$ can only be incremented by 1.